Single-quasiparticle Excitations Research Articles

Lieb-Robinson correlation function for the quantum transverse-field Ising model

The Lieb-Robinson correlation function is the norm of a commutator between local operators acting on separate subsystems at different times. This provides a useful state-independent measure for characterizing the specifically quantum interaction between spatially separated qubits. The finite propagation velocity for this correlator defines a “light cone” of quantum influence. We calculate the Lieb-Robinson correlation function for one-dimensional qubit arrays described by the transverse-field Ising model. Direct calculations of this correlation function have been limited by the exponential increase in the size of the state space with the number of qubits. We introduce a technique that avoids this barrier by transforming the calculation to a sum over Pauli walks which results in linear scaling with system size. We can then explore propagation in arrays of hundreds of qubits and observe the effects of the quantum phase transition in the system. We observe the emergence of two distinct velocities of propagation: a correlation front velocity, which is affected by the phase transition, and the Lieb-Robinson velocity which is not. The correlation front velocity is equal to the maximum group velocity of single quasiparticle excitations. The Lieb-Robinson velocity describes the extreme leading edge of correlations when the value of the correlation function itself is still very small. For the semi-infinite chain of qubits at the quantum critical point, we derive an analytical result for the correlation function. Published by the American Physical Society 2024

Single-quasiparticle eigenstate thermalization.

Quadratic Hamiltonians that exhibit single-particle quantum chaos are called quantum-chaotic quadratic Hamiltonians. One of their hallmarks is single-particle eigenstate thermalization introduced in Łydżba etal. [Phys. Rev. B 104, 214203 (2021)2469-995010.1103/PhysRevB.104.214203], which describes statistical properties of matrix elements of observables in single-particle eigenstates. However, the latter has been studied only in quantum-chaotic quadratic Hamiltonians that obey the U(1) symmetry. Here, we focus on quantum-chaotic quadratic Hamiltonians that break the U(1) symmetry and, hence, their "single-particle" eigenstates are actually single-quasiparticle excitations introduced on the top of a many-body state. We study their wave functions and matrix elements of one-body observables, for which we introduce the notion of single-quasiparticle eigenstate thermalization. Focusing on spinless fermion Hamiltonians in three dimensions with local hopping, pairing, and on-site disorder, we also study the properties of disorder-induced near zero modes, which give rise to a sharp peak in the density of states at zero energy. Finally, we numerically show equilibration of observables in many-body eigenstates after a quantum quench. We argue that the latter is a consequence of single-quasiparticle eigenstate thermalization, in analogy to the U(1) symmetric case from Łydżba etal. [Phys. Rev. Lett. 131, 060401 (2023)0031-900710.1103/PhysRevLett.131.060401].

Current noise and Keldysh vertex function of an Anderson impurity in the Fermi-liquid regime

We present a complete microscopic Fermi-liquid description for next-to-leading order transport through an Anderson impurity under a finite bias voltage $V$. It is applicable to multilevel quantum dots without particle-hole or time-reversal symmetry and is constructed based on the nonequilibrium Keldysh formalism, taking into account the current conservation between electrons in the impurity levels and the conduction bands. Specifically, we derive the formula for the current noise generated in the steady flow up to terms of order ${(eV)}^{3}$ at zero temperature $T=0$. To this end, we calculate the Keldysh vertex functions ${\mathrm{\ensuremath{\Gamma}}}_{\ensuremath{\sigma}{\ensuremath{\sigma}}^{\ensuremath{'}};{\ensuremath{\sigma}}^{\ensuremath{'}}\ensuremath{\sigma}}^{{\ensuremath{\nu}}_{1}{\ensuremath{\nu}}_{2};{\ensuremath{\nu}}_{3}{\ensuremath{\nu}}_{4}}(\ensuremath{\omega},{\ensuremath{\omega}}^{\ensuremath{'}};{\ensuremath{\omega}}^{\ensuremath{'}},\ensuremath{\omega})$, which depend on branches ${\ensuremath{\nu}}_{1},\phantom{\rule{4pt}{0ex}}{\ensuremath{\nu}}_{2},\phantom{\rule{4pt}{0ex}}{\ensuremath{\nu}}_{3}$, and ${\ensuremath{\nu}}_{4}$ of the time-loop contour and on spin degrees of freedom $\ensuremath{\sigma}$ and ${\ensuremath{\sigma}}^{\ensuremath{'}}$, up to linear order terms with respect to $eV$, $T$, and frequencies $\ensuremath{\omega}$ and ${\ensuremath{\omega}}^{\ensuremath{'}}$. The coefficients of these linear order terms are determined by a set of the parameters, defined with respect to the equilibrium ground state: the phase shift, static susceptibilities, and nonlinear three-body susceptibilities of the impurity electrons. The low-energy expressions of the vertex components are shown to satisfy the Ward identities with the Keldysh Green's functions expanded up to terms of order ${\ensuremath{\omega}}^{2}$, ${(eV)}^{2}$, and ${T}^{2}$. We also find that the imaginary part of the Ward identities can be described in terms of the $eV$-dependent collision integrals for a single-quasiparticle excitation and that for a single quasiparticle-quasihole pair excitation. These collision integrals ensure the current conservation of the next-to-leading order Fermi-liquid transport due to the quasiparticles with a finite damping rate.

Diffusion in generalized hydrodynamics and quasiparticle scattering

We extend beyond the Euler scales the hydrodynamic theory for quantum and classical integrable models developed in recent years, accounting for diffusive dynamics and local entropy production. We review how the diffusive scale can be reached via a gradient expansion of the expectation values of the conserved fields and how the coefficients of the expansion can be computed via integrated steady-state two-point correlation functions, emphasising that {\mathcal PT}𝒫T-symmetry can fully fix the inherent ambiguity in the definition of conserved fields at the diffusive scale. We develop a form factor expansion to compute such correlation functions and we show that, while the dynamics at the Euler scale is completely determined by the density of single quasiparticle excitations on top of the local steady state, diffusion is due to scattering processes among quasiparticles, which are only present in truly interacting systems. We then show that only two-quasiparticle scattering processes contribute to the diffusive dynamics. Finally we employ the theory to compute the exact spin diffusion constant of a gapped XXZ spin-1/2−1/2 chain at finite temperature and half-filling, where we show that spin transport is purely diffusive.

Conformal Data and Renormalization Group Flow in Critical Quantum Spin Chains Using Periodic Uniform Matrix Product States.

We establish that a Bloch-state ansatz based on periodic uniform matrix product states (PUMPS), originally designed to capture single-quasiparticle excitations in gapped systems, is in fact capable of accurately approximating all low-energy eigenstates of critical quantum spin chains on the circle. When combined with the methods of [Milsted and Vidal, Phys. Rev. B 96, 245105PRBMDO2469-995010.1103/PhysRevB.96.245105] based on the Koo-Saleur formula, PUMPS Bloch states can then be used to identify each low-energy eigenstate of a chain made of up to hundreds of spins with its corresponding scaling operator in the emergent conformal field theory (CFT). This enables the following two tasks that we demonstrate using the quantum Ising model and a recently proposed generalization thereof due to O'Brien and Fendley [Phys. Rev. Lett. 120, 206403]. (i)From the spectrum of low energies and momenta we extract conformal data (specifying the emergent CFT) with unprecedented numerical accuracy. (ii)By changing the lattice size, we investigate nonperturbatively the renormalization group flow of the low-energy spectrum between two CFTs. In our example, where the flow is from the tricritical Ising CFT to the Ising CFT, we obtain excellent agreement with an analytical result [Klassen and Melzer, Nucl. Phys. B370, 51110.1016/0550-3213(92)90422-8] conjectured to describe the flow of the first spectral gap directly in the continuum.

Fermi liquid theory applied to a film on an oscillating substrate

We have studied the transmission of transverse oscillations through a thin Fermi liquid film, using Landau's Fermi liquid theory. Fermi liquid theory describes the dynamics of interacting, degenerate fermion systems, for example non-superfluid, i.e.\ normal state \textsuperscript{3}He at millikelvin temperatures. The response of a Fermi liquid to the transverse oscillations of a planar substrate has previously been calculated for a fluid layer of infinite thickness. We have modified these calculations for application to a film of finite thickness, either with a free surface, or as confined between two parallel substrates. The equations take into account contributions to the acoustic impedance from both the collective transverse zero sound mode, as well as the incoherent single-quasiparticle excitations and are solved using numerical methods.

Single to Multiquasiparticle Excitations in the Itinerant Helical Magnet CeRhIn(5).

CeRhIn(5) is an itinerant magnet where the Ce(3+) spins order in a simple helical phase. We investigate the spin excitations and observe sharp spin waves parameterized by a nearest-neighbor exchange, J(RKKY)=0.88±0.05 meV. At higher energies, the spin fluctuations are heavily damped, where single-quasiparticle excitations are replaced by a momentum- and energy-broadened continuum constrained by kinematics of energy and momentum conservation. The delicate energy balance between localized and itinerant characters results in the breakdown of the single-quasiparticle picture in CeRhIn(5).

Spectral analysis on a phonon spectral function of a solid-state plasma in a doped semiconductor

We report an analysis on a phonon spectral function of a solid-state plasma formed in a doped semiconductor. Real and imaginary parts of phonon propagators are evaluated including carrier screening effects within a random phase approximation, and finite-temperature spectral behavior of the phonon spectral function is examined in terms of plasmon-phonon coupled modes and quasiparticle excitation mode of the plasma. The results are applied to the case of conduction electrons in a wurtzite GaN considering carrier-phonon coupling channel via polar optical phonons. We show that the dispersion relations of the plasmon-LO phonon coupled (‘upper’ and ‘lower’) modes and the character of the additional modes via single quasiparticle excitations are heavily associated with the nonlocal and dynamic behavior of the energy shift and collisional broadening of the dressed phonon propagator of the plasma.

Charge separation at nanoscale interfaces: energy-level alignment including two-quasiparticle interactions.

The universal and fundamental criteria for charge separation at interfaces involving nanoscale materials are investigated. In addition to the single-quasiparticle excitation, all the two-quasiparticle effects including exciton binding, Coulomb stabilization, and exciton transfer are considered, which play critical roles on nanoscale interfaces for optoelectronic applications. We propose a scheme allowing adding these two-quasiparticle interactions on top of the single-quasiparticle energy level alignment for determining and illuminating charge separation at nanoscale interfaces. Employing the many-body perturbation theory based on Green's functions, we quantitatively demonstrate that neglecting or simplifying these crucial two-quasiparticle interactions using less accurate methods is likely to predict qualitatively incorrect charge separation behaviors at nanoscale interfaces where quantum confinement dominates.

Excitation of Single Quasiparticles in a Small Superconducting Al Island Connected to Normal-Metal Leads by Tunnel Junctions

We investigate the dynamics of individual quasiparticle excitations on a small superconducting aluminum island connected to normal metallic leads by tunnel junctions. We find the island to be free of excitations within the measurement resolution. This allows us to show that the residual heating, which typically limits experiments on superconductors, has an ultralow value of less than 0.1 aW. By injecting electrons with a periodic gate voltage, we probe electron-phonon interaction and relaxation down to a single quasiparticle excitation pair, with a measured recombination rate of 16 kHz. Our experiment yields a strong test of BCS theory in aluminum as the results are consistent with it without free parameters.

Coulomb energy and gluon distribution in the presence of static sources

We compute the energy of the ground state and a low lying excitation of the gluonic field in the presence of static quark -anti-quark ($\qq$) sources. We show that for separation between the sources less then a few fm the gluonic ground state of the static $\qq$ system can be well described in terms of a mean field wave functional with the excited states corresponding to a single quasi-particle excitation of the gluon field. We also discuss the role of many particle excitations relevant for large separation between sources.

Quantal Andreev billiards: Density of states oscillations and the spectrum-geometry relationship

Andreev billiards are finite, arbitrarily shaped, normal-state regions, surrounded by superconductor. At energies below the superconducting energy gap, single-quasiparticle excitations are confined to the normal region and its vicinity, the mechanism for confinement being Andreev reflection. Short-wave quantal properties of these excitations, such as the connection between the density of states and the geometrical shape of the billiard, are addressed via a multiple scattering approach. It is shown that one can, inter alia, ``hear'' the stationary chords of Andreev billiards.

QUANTAL ANDREEV BILLIARDS: SEMICLASSICAL APPROACH TO MESOSCALE OSCILLATIONS IN THE DENSITY OF STATES

Andreev billiards are finite, arbitrarily-shaped, normal-state regions, surrounded by superconductor. At energies below the superconducting gap, single-quasiparticle excitations are confined to the normal region and its vicinity, the essential mechanism for this confinement being Andreev reflection. This Paper develops and implements a theoretical framework for the investigation of the short-wave quantal properties of these single-quasiparticle excitations. The focus is primarily on the relationship between the quasiparticle energy eigenvalue spectrum and the geometrical shape of the normal-state region, i.e. the question of spectral geometry in the novel setting of excitations confined by a superconducting pair-potential. Among the central results of this investigation are two semiclassical trace formulas for the density of states. The first, a lower-resolution formula, corresponds to the well-known quasiclassical approximation, conventionally invoked in settings involving superconductivity. The second, a higher-resolution formula, allows the density of states to be expressed in terms of: (i) An explicit formula for the level density, valid in the short-wave limit, for billiards of arbitrary shape and dimensionality. This level density depends on the billiard shape only through the set of stationary-length chords of the billiard and the curvature of the boundary at the endpoints of these chords; and (ii) Higher-resolution corrections to the level density, expressed as a sum over periodic orbits that creep around the billiard boundary. Owing to the fact that these creeping orbits are much longer than the stationary chords, one can, inter alia, "hear" the stationary chords of Andreev billiards.

Thermodynamic properties in the evolution from BCS to Bose-Einstein condensation for ad-wave superconductor at low temperatures

The low-temperature evolution from BCS to Bose-Einstein condensation (BEC) for a two-dimensional d-wave superconductor is discussed at the saddle point (mean field) level. A systematic study of the changes of low-temperature thermodynamic properties is presented as a function of the charge carrier density and fixed interaction. It has been found that when the interaction strength is large enough, there is a critical density below which the single quasiparticle excitation spectrum develops a gap. At higher density of carriers and lower interaction strength (towards the BCS regime) the superconductor has gapless quasiparticle excitations, while at lower densities and higher interactions (towards the BEC regime) quasiparticle excitations are fully gapped. The appearence of a full gap in the quasiparticle excitation spectrum has dramatic consequences to the compressibility, specific heat, and spin susceptibility at low temperatures, as the critical density ${n}_{c}$ is crossed. The change in behavior of these quantities indicates a possible quantum phase transition between a d-wave gapless phase and a d-wave fully gapped phase, as ${n}_{c}$ is crossed.

Variational theory of bulk4Hewith shadow wave functions: Ground state and the phonon-maxon-roton spectrum

We apply an efficient optimization scheme to shadow wave functions (SWF's) for the ground state of liquid and solid ${}^{4}\mathrm{He}$. Results improve on previous variational energies in both phases. In the liquid, the gain over a wave function with only pair and triplet correlations increases with density, providing a quantitative estimate of the increasing effect of higher-order correlations. The discrepancy with the exact ground-state energy is nearly constant over a wide range of densities, yielding excellent estimates for the equilibrium, freezing, and melting densities. The optimal SWF's can be represented with high precision by density-independent sets of variational parameters for the liquid and the solid phases. An extensive study of ground-state properties demonstrates the uniformly good quality of the variational description afforded by the optimized SWF's. Based on such an accurate representation of the ground state, and including the correct long-range correlations due to the zero-point motion of phonons, we compute the excitation spectrum and the strength of the single quasiparticle excitation peak. While the use of optimized SWF's confirms the accuracy of previous studies in the maxon-roton region, the proper treatment of long-range correlations allows us to extend to the phonon region the agreement between theory and experiment. We simulate relatively large systems in order to explore the long-wavelength regime in detail. Even down to wave vectors where the excitation energy exhibits a highly linear dispersion, which would suggest a harmonic phonon mode, the kinetic and potential energies of the excitation are far from verifying equipartition. This result is supported by additional diffusion Monte Carlo simulations within the fixed node approximation. We locate the onset of the harmonic regime for the long-wavelength excitations at an extremely small value of the wave vector, $k\ensuremath{\lesssim}0.05 {\mathrm{\AA{}}}^{\ensuremath{-}1}$.

Acoustic-plasmon branches in photoexcited semiconductors

We analyze the spectra of electronic elementary excitations in a double component plasma of photoinjected electrons and holes in semiconductors under continuous laser illumination. We show that in the resulting nonequilibrium steady state four types of elementary excitations of the photoinjected carrier system can be identified. Two are the expected single quasi-particle excitations and the higher frequency plasma wave, and two novel ones at low frequencies labelled as acoustic plasma waves that are well defined under particular conditions. These acoustic branches are interpreted as corresponding to the collective motion of each type of carriers interacting through the screened part of Coulomb interaction.

Photoinjected carrier's acoustic plasma oscillations

Resorting to the Nonequilibrium Statistical Operator Method (NSOM) we calculate the Raman spectrum of the double (electrons and holes) photoinjected plasma in direct-gap polar semiconductors. It allows us to identify four types of elementary excitations in the photoexcited carrier system. Besides the expected Raman bands corresponding to single quasi-particle excitations and a higher frequency plasma wave (labelled optical), there appear two low-frequency bands. They show a linear energy dispersion relation and are labelled acoustic plasma oscillations. While the optical plasma branch is ascribed to the out of phase collective movement of both types of carriers interacting through the bare Coulomb interaction, the acoustic branches are ascribed to the in-phase oscillation of each type of carriers interacting through the screened part of Coulomb interaction.

Transverse acoustic impedance of normal liquid3He

Both the real and imaginary parts of the transverse acoustic impedance of normal liquid3He have been measured at excitation frequencies of 10 and 30 MHz, fluid pressures from 0.7 to 27 bar, and temperatures from 3 mK to 1 K. The impedance is obtained from the changes in resonance frequency and Q of a quartz crystal, which is electrically driven to oscillate in a thickness shear mode while immersed in liquid3He. These results are compared with the predictions of Fermi liquid theory, which takes into account two contributions to the impedance: (1) incoherent single-quasiparticle excitations, and (2) the excitation of the collective transverse sound mode. At 0.7 bar, our measurements of the impedance are in agreement with the predictions of Fermi liquid theory and imply that the symmetric Fermi liquid parameterF2=1.25±0.4 ifF1=6.3. At higher pressures, we also observe agreement in the region ωτ<0.3, where ω is the excitation frequency and τ is the quasiparticle scattering time. However, above 8 bar in the zero-sound regime (ωτ≳1), the impedance is observed to be frequency dependent, at constant ωτ. This frequency dependence cannot be explained within the present framework of Fermi liquid theory.

Variational calculations of the excited states of liquidHe4

Approximate wave functions of the form $\mathcal{G}\ensuremath{\Phi}(n(\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}}))$, where $\mathcal{G}$ is a correlation operator that contains two-body, three-body, and momentum-dependent correlations, and $\ensuremath{\Phi}(n(\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}}))$ is a noninteracting-Bose-gas wave function with occupation numbers $n(\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}})$, are used to calculate the energies of excited states of liquid $^{4}\mathrm{He}$. The energy expectation values are calculated by generalizing the Fermi hypernetted-chain methods. The single-quasiparticle excitation spectrum provides stringent tests for the correlation operator $\mathcal{G}$. The calculated phonon, maxon spectra are not in good agreement with the experimental results presumably because of the truncations in the large-distance behavior of the two-body correlations in the $\mathcal{G}$. The results obtained for the roton energies are in good agreement with the experiments over the range of liquid-$^{4}\mathrm{He}$ density.

Phase Transitions in Nuclear Fission. II

The nucleus immediately after the second saddle point in a dumbbell structure is described in terms of two nuclear clusters linked by quasiparticle exchange. The itinerant quasiparticles near the Fermi surface are designed to resolve the inconsistency between the alternative models of nuclear fission, the shell model and the cluster model. The effective residual interaction operative between quasiparticles comprises long-range and short-range parts, the former originating from the exchange coupling of the two forming clusters and the latter from the pairing interaction. The condensed state at low excitation energies is then characterized by the corresponding order parameters, mass asymmetry between two clusters and the energy gap in the single-quasiparticle excitation spectrum. Each order parameter displays a continuous behaviour at a transition point, indicating a phase transition of the second kind. In the condensed phase, short-range order carries on an active competition against long-range order. Under certain conditions there occurs saturation mass asymmetry in the ground state which leads to the production of the closed shell fragment. A discussion is devoted to the current-carrying state which may play a role in fission and furnish an explanation of the mass asymmetry.